1. Correlations of Electrons in Magnetic Fields
전건상
이화여자대학교
, POSTECH 물리학과 Colloquium

2. Hall effect

3. Classical & quantum Hall effect
(Classical) Hall effect
Quantized Hall effect ?

4. 2D electron gas – GaAs heterostructure

5. Landau levels

6. Integral quantum Hall effect
von Klitzing, Dorda, Popper (1980)

7. Explanation of IQHE

8. Berry phase and Chern number
Berry curvature of energy bands
Hall conductivity
: topologically protected, rather insensitive to details
Thouless, Kohmoto, Nightingale, den Nijs (1982)

9. Fractional quantum Hall effect
Tsui, Stormer, Gossard (1982)

10. Fractional quantum Hall effect
[Du,Stormer,Tsui,Pfeiffer,West (1993)]

11. Trial wave function at 1/3-filling

12. Hierarchy scenario
Quasiholes and quasiparticles condense to new FQHE states
Relative intensity is inconsistent with experiments.
Haldane(1983), Halperin(1984)

13. Composite fermions IQHE of composite fermions → FQHE of electrons
Jain(PRL,1989)

14. Fractions observed
Consistent with composite fermions in fractions and stability

15. New fractions observed
FQHE of composite fermions?
Pan,Stormer,Tsui,Pfeiffer,Baldwin,West (PRL,2003)

16. FQHE : n=1 Landau Level
Xia,Pan,Vicente,Adams,Sullivan,Stormer,Tsui,Pfeiffer,Baldwin,West (PRL,2004)
Fogler, Koulakov, Shklovskii (PRL,1996)

17. Even Denominator: ν=1/2

18. Even denominator: higher LL
Cooper pairing for p-wave bound state of composite fermions at n=1 LL
Scarola, Park, Jain (Nat,2000)
Xia,Pan,Vicente,Adams,Sullivan,Stormer,Tsui,Pfeiffer,Baldwin,West (PRL,2004)
Eisenstein, Cooper, Pfeiffer, West (PRL,2002)

19. Composite fermions at zero effective magnetic field
Scarola, Park, Jain (Nat,2000)

20. Topological quantum computations
Use topological properties of non-abelian FQHE at ν=5/2 LL
“qubit” = non-local entity composed of several well-separated quasiparticles
Advantage: more stable against decoherence
das Sarma, Freedman, Nayak (PRL,2005);(PT,2006)
Read (PT,2012)

21. Quantum Hall effect in graphene
Novoselov,Geim,Morozov,Jiang,Katsnelson,Grigorieva,Dubonos,Firsov (Nat,2005)
Zhang,Tan,Stormer,Kim (Nat,2005)

22. FQHE in graphene Bolotin,Ghahari,Shulman,Stormer,Kim (Nat,2009)
Du,Skachko,Duerr,Luican,Andrei (Nat,2009)

23. Black Phosphorous
Li,Yang,Ye,Zhang,Zhu,Lou,Zhou,Li,Watanabe,Taniguchi,Chang,Wang,Chen,Zhang (NN,2016)
Li,Yu,Ye,Ge,Ou,Wu,Feng,Chen,Zhang (NN,2014)

24. MgZnO/ZnO 2DES
Tsukazaki,Akasaka,Nakahara,Ohno,Ohno,Maryenko,Ohtomo,Kawasaki (NM,2010)
Falson,Maryenko,Friess,Zhang,Kozuka,Tsukazaki,Smet,Kawasaki (NP,2015)

25. Anisotropy of electronic band
Band mass anisotropy
Reflected in Fermi surface at zero field
Reflected in Landau states with finite magnetic fields
Composite fermions under high fields
induced by isotropic interactions

26. Role of anisotropy of electronic band
Jo,Rosales,Mueed,Pfeiffer,West,Baldwin,Winkler,Padmanabhan,Shayegan (PRL,2017)

27. Role of anisotropy of electronic band
DMRG calculation
variational CF wave function Coulomb interaction
Interplay of correlations and band anisotropy
Ippoliti,Geraedts,Bhatt (PRB,2017); Jeon,Balram,Jain (in prep.)

28. International System of Units
Newell (PT,2014); Knotts,Mohr,Phillips (2017)

29. New SI base quantities Effective May 20, 2019
Newell (PT,2014); Knotts,Mohr,Phillips (2017)

30. Josephson and von Klitzing constants
Newell (PT,2014)

31. Von Klitzing constant: GaAs/AlGaAs vs. Graphene
Janssen,Fletcher,Goebel,Williams,Tzalenchuk,Yakimova,Kubatkin,Lara-Avilla,Falko (NJP,2011)

32. Watt Balance and the kilogram
𝑎 𝐵𝐼𝐿=𝑚𝑔
𝑏 𝐵𝐿𝑣= 𝑉 2
𝑎 & 𝑏 𝑚= 𝐼 𝑉 2 𝑔𝑣
4th generation Watt balance, NIST-4: absolute uncertainty less than 20μg for 1kg
Newell (PT,2014)

33. ADDITIONAL HALL EFFECTS?

34. Quantum spin Hall effects
Finite band gap in the bulk
Two bands localized at the edges traverse the gap
Strong spin-orbit coupling
Spin-filtered nonchiral edge states: electrons with opposite spin propagate in opposite directions
topological insulator with Z2 topological order
Kane, Mele (PRL,2005)

35. QSHE: HgTe quantum well
König,Wiedmann,Brüne,Roth,Buhmann,Molenkamp,Qi,Zhang (Sci,2007)

36. Bismuthen: Room-temperature QSHE?
Reis,Li,Dudy,Bauernfeind,Glass,Hanke,Thomale,Schäfer,Claessen (Sci,2017)

37. Quantum anomalous Hall effect
quantized Hall transport without magnetic field
ferromagnetic insulating material
+ topologically nontrivial band structure
V-doped (Bi,Sb)2Te3
Chang,Zhao,Kim,Zhang,Assaf,Heiman,Zhang,Liu,Chan,Moodera (PRL,2015)
Chang,Zhang,Feng,Shen,Zhang,Guo,Li,Ou,Wei,Wang,Ji,Feng,Ji,Chen,Jia,Dai,Fang,Zhang,He,Wang,Lu,Ma,Xue (Sci,2013)

38. Quantum valley Hall effect
AB-BA domain walls with external electric fields
Topologically protected valley polarized chiral modes
Maximum conductance ~ two quantum conductance
Decrease of conductance with mean free path 420nm
Vaezi,Liang,Ngai,Yang,Kim(PRX,2013)
Ju,Shi,Nair,Lv,Jin,Velasco,Ojeda-Aristizabal,Bechtel,Martin,Zettl,Analytis,Wang (Nat,2015)

39. Concluding…
QHE, FQHE, composite fermions in semiconductor, graphene, vdw material, oxide …
Topological computation, new SI, anisotropy,…
Quantum (spin, anomalous, valley,…) Hall effects …

40. Concluding … 2D Library “Lego” on atomic scale
Geim, Grigorieva (Nat,2013)